Place the chicken breasts in a large ziptop bag. Add the balsamic vinegar, Italian seasoning and some salt and pepper to the bag. Pour the reserved pepper oil, olive brine and tomato oil into the bag. Seal the bag and gently massage the chicken to combine the marinade ingredients.
Preheat a grill or grill pan over medium-high heat. Toss the artichoke hearts and zucchini strips with the olive oil in a large bowl. Season with salt and pepper. Toss until evenly coated. Spray the grill with nonstick cooking spray and place the artichokes and zucchini on the grill. Cook, without flipping, until the vegetables have even grill marks, 4 to 5 minutes per side. Transfer to a cutting board to cool slightly. Cut the zucchini into 1/2-inch pieces and quarter the artichoke hearts. Place the grilled vegetables back into the same large bowl. Add the roasted red pepper strips, olives and sun-dried tomatoes.
Remove the chicken from the bag and discard the marinade. Grill the chicken until it reaches an internal temperature of 160 degrees F (the chicken will reach 165 degrees F as it rests), 6 to 8 minutes per side. Transfer to a cutting board to rest for 2 minutes.
Slice the chicken into chunks and add to the bowl. Tear the basil leaves into the bowl and gently toss to combine the mixture. Serve immediately over butter lettuce leaves.